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Mathematics > Optimization and Control

arXiv:2406.03504 (math)
[Submitted on 3 Jun 2024]

Title:A New Branch-and-Bound Pruning Framework for $\ell_0$-Regularized Problems

Authors:Theo Guyard, Cédric Herzet, Clément Elvira, Ayşe-Nur Arslan
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Abstract:We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions through "pruning tests". In standard implementations, evaluating a pruning test requires to solve a convex optimization problem, which may result in computational bottlenecks. In this paper, we present an alternative to implement pruning tests for some generic family of $\ell_0$-regularized problems. Our proposed procedure allows the simultaneous assessment of several regions and can be embedded in standard BnB implementations with a negligible computational overhead. We show through numerical simulations that our pruning strategy can improve the solving time of BnB procedures by several orders of magnitude for typical problems encountered in machine-learning applications.
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG)
Cite as: arXiv:2406.03504 [math.OC]
  (or arXiv:2406.03504v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2406.03504

Submission history

From: Theo Guyard [view email]
[v1] Mon, 3 Jun 2024 19:40:06 UTC (563 KB)
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